Axisymmetric capillary bridges of soft solids with surface elasticity

It is well known that axisymmetric liquid capillary bridges between two rigid surfaces have menisci shapes with constant total curvature in space that is determined by the volume of liquid in the bridge and the contact angles. The shapes are a direct outcome of the fact that surface stresses on a liquid surface are isotropic and depend on only one measurable scalar material property, namely, the surface energy. Capillary bridges of soft solids, on the other hand, are expected to evolve different shapes than their liquid counterparts firstly, because any deformation of the surface is opposed by the elasticity of the bulk. This competition is more intense when the length scales associated with the bridge are small or equivalently, the ratio of strain energies stored by surface to the bulk is large. Secondly, recent experiments have shown that surfaces of soft solids can be significantly sensitive to surface strains even at length scales of tens of microns. We have performed carefully designed Finite Element simulations considering finite deformations of both the bulk and the surface to understand the evolution of the shapes of solid menisci when the capillary bridge is in equilibrium and when it is stretched uniaxially. Our results show that in equilibrium, the shape of the meniscus of a soft solid capillary with significant surface elasticity is very unlike that of a liquid. However, when the bridge is stretched, the meniscus tends to attain a constant total curvature and behave like a liquid bridge with a high effective surface energy.